I'm assuming that this project is on some sort of budget.
I'd pick something not horribly expensive -your money would be better spent in software rather than tires. Having spent a fair bit of time driving about the Mojave Desert, I'd have to echo AlaskaVX's comment about flotation -fatter the better. The MT Bajas are reasonably priced, and offer excellent sand traction. Your speed(s) and route will not likely take you across tire-puncturing terrain, so just steer clear of any brush and mountains and your tires should be fine. You can add a can of Fix-A-Flat to each one to give you piece of mind.
Your robot's biggest enemies will be heat and vibration. Heat can be beat with a fair amount of A/C, but the VX is a well-known rump-shaker. Since plush suspensions aren't my thing, I'll have to hand that one off.